''<knowledge of the universe as a whole can not be obtained by metaphysics>''

+

Many metaphysical writers attempt to show from a priori principles some grand design to explain the nature of the world. In modern philosophy Hegel has been an influential example of this practice. Russell believes that such attempts are futile and that examining Hegel's system gives us some in sight as to why.

−

''<Hegel was a chief advocate of using metaphysics to construct a system of the universe>''

+

Russell's interpretation of Hegel, which he believes is widely held, is that ''everything short of the Whole is obviously fragmentary, and obviously incapable of existing without the complement supplied by the rest of the world.'' Both the world of things and the world of thought exhibit this fragmentary nature. In the world of things each thing seems to imply something larger and as we seek to understand the larger thing we eventually arrive at the universe as a whole. In the world of thought, the incompleteness appears as contradictions giving rise to the cycle of thesis anti-thesis and synthesis (the famous Hegelian Dialectic). Following this dialectic to its conclusion leads to the "Absolute Idea" which describes reality. This reality is ''one single harmonious system, not in space or time, not in any degree evil, wholly rational, and wholly spiritual.''

+

The flaw in Hegel's argument is equivocation with respect to the idea of the nature of things. Hegel uses the nature of things both to mean all the truths of something and the thing itself. To explain Russell gives an example of a tooth ache. The sufferer knows the nature of the tooth ache in a way the dentist does not. The sufferer does not know many of the truths about the tooth ache that the dentist does. It does not follow that the sufferer does not know the nature of the tooth ache because he or she does not know all the truths about the tooth ache.

−

''<A summary of a summary of a complex system - incompleteness. thesis, antithesis, synthesis and the absolute idea>''

+

Russell criticizes Hegel and others who start off with a view to prove and then construct a system to prove it. These philosophers try to show that some perceived aspect of reality is actually contradictory. But as knowledge advances, we find again and again that the contradictions vanish and with them the a priori knowledge of the world proposed by the philosopher.

−

''<the central tenant of Hegel's philosophy and the confusion of the term "nature of things">''

+

Kant is another example of a philosopher that reasons that some aspect of reality is self contradictory. His target was space-time. Because apparent space and time are infinitely large and infinitely small, the seem to present contradictions. Infinity was very problematic for mathematicians and philosophers until the late 19th century. Kant, writing in the 18th century, saw these apparent contradictions and proposed that our experience of space-time was subjective. But infinity is not self contradictory and Kant's interpretation of space-time now appears to be incorrect.

−

''<the universe can not be shown to be an harmonious whole by Hegel's argument>''

−

−

''<past arguments against realities of the apparent world are being disputed and dismissed by contemporary philosophy and science>''

Executive Summary

This book is an introduction to philosophy. In it the eminent British philosopher, Bertrand Russell, explores what we can know, and how philosophy helps us to identify and classify knowledge and uncertainty. In the opening chapters, we learn how to use inquiry and analysis to understand the basic question of epistemology. As we gain a foothold in the subject, we are introduced to the ideas of leading thinkers in western philosophy. Russell acquaints us with the rationalism, empiricism and idealism. As he does so we see what he thinks are most valuable concepts from each school of thought. The book also argues for the value of philosophy both as an enriching study for individuals as well as an asset to society. The entire text is available at Gutenberg.org

Chapter Summaries

Preface

In the four sentence preface Russell commits to saying something constructive and therefore confining himself primarily to epistemology. He credits G. E. Moore, J. M. Keynes and Gilbert Murray for their contributions.

Appearance and Reality

In seeking certainty, we discover vagueness and confusion in many common ideas. The search for certainty launches us into the study of philosophy.

One area that seems to grant us certainty is our immediate experience. Russell describes his immediate experience as he sits in a sunny room at his desk. He focuses on the sensations he experiences of the table before him. In a precise description of its visual appearance Russell notes that although he believes the table to be all one color, that part of the table appears almost white due to the reflected light. He knows that if he moves that the apparent whiteness of the part of the table will move, too. Although this difference in appearance is unimportant for most practical purposes, the artist must learn to see and portray things as they appear, rather than as they "really" are. Philosophy too, guides us to examine closely what we experience.

Examining the color of the table, we are lead to the conclusion that there is no color which is preeminently the color of the table. The color depends on the presence and kind of artificial light, the time of day and the condition of the viewers eyes, among many other factors.

The texture of the table presents a similar result. Although to the unaided eye the table appears smooth, with a magnifying glass, ridges and rough spots become evident. More powerful magnification would reveal an even more elaborate texture. Which is the true texture? There is no reason to pick one over the other.

The sense of touch does not give us any more certainty about the real nature of the table. Examining the sensations we experience about the table we must conclude that we only know about its appearance. "The real table, if there is one, is not immediately known to us at all, but must be an inference from what is immediately known."

Russell then introduces us to Bishop Berkley, who showed that matter can be denied without absurdity. He concludes the chapter by pointing out that philosophy guides us to from the common place to the amazing in quick order. Our inquiry into the certainty provided by our immediate experience leads us to realize that the appearance of matter can not be the same as its reality. The next question Russell addresses is does matter exist?

The Existence of Matter

Since our immediate experience gives us no certainty about the existence of matter and since it is possible to deny the existence of matter without logical fallacy, should we assume that matter does not exist? Russell answers no. The existence of matter is the simplest explanation of our experience.

Russell asks us to consider a cat. He asks to imagine that he sees a cat at one moment in one part of the room and in another somewhere else. Our simplest assumption is that the cat has moved. But if there is no matter and nothing but Russell's sensations, then the cat can not have been anywhere he did not see it. It must have ceased to exist when it passed out of his view and reappeared when he saw it in its new location. Now imagine that his cat is acting hungry. How could this be accounted for? No hunger can exist except his own sensation of hunger. Any explanation of this behavior that does not suppose the existence of a real cat is bound to be more complicated than assuming that the cat does exist outside the sensations Russell is experiencing.

But the problem of the cat is minor compared to the problem of explaining other people. When some one speaks and we hear sounds we associated with ideas and we see the persons face, it is difficult to imagine that they are not expressing a thought, as we would be if we were to make similar sounds.

We are certain of our sensations regarding matter and those sensations seem to have agreement with each other about objects of our experience. Common sense tells us that there is a source of these sensation external to us. We would never have doubted that matter existed if we had not begun an analysis of appearance and reality. Although this argument is not convincing, taken with the argument for the existence of matter as the simplest explanation, it does urge us to accept we previously naturally believed.

The argument for the existence of matter is not decisive. There is room for doubt. This is the nature of philosophical knowledge. Such knowledge is built up from instinctive beliefs that we hold most strongly. "...each as much isolated and as free from irrelevant additions as possible. It should take care to show that, in the form in which they are finally set forth, our instinctive beliefs do not clash, but form a harmonious system." Such a harmonious system, though it may contain error, is less likely to be incorrect, because of the interrelationship of the parts and the scrutiny given to each part.

The Nature of Matter

Having established, at least to some degree of certainty, that matter exists, what can we know of its nature? The physical sciences tells us that matter is wave-motion in space. This wave-motion is not identical to our experience but corresponds to it. For example, if we see a red object and a blue object we know that there is some corresponding difference between the two objects that give rise to the different sensations. Likewise, if we see two blue objects we may assume that there is some common property in the two objects that gives us the sensation of blueness.

We experience space through our sense of touch and our sense of sight. We learn in infancy how to associate these two sensations to create an internal sense of the space we perceive. Science and common sense assume that there is a public space in which objects exist. "It is this physical space which is dealt with in geometry and assumed in physics and astronomy." As with our experience of matter, our experience of space is one of correspondence. We do not experience the intrinsic nature of space.

Some philosophers contend that we can know something of the intrinsic nature of matter. They make this claim because although our sensations do point to something that exists independently of us, that something is mental. These philosophers are called idealists.

Idealism

Idealism is a widely held doctrine in philosophy and so demands some attention. Russell defines idealism as "the doctrine that whatever exists, or at any rate whatever can be known to exist, must be in some sense mental." This doctrine is presented in the context of discussions about what is required for something to be known.

The first philosopher to argue for idealism was Bishop Berkley, who Russell introduced in Chapter 1 "Appearance and Reality". Berkley's argument is that our sensations must be in our minds and do not have any existence apart from us. Our sensations are all that we can know and to be known is to be in a mind. The conclusion of Berkley's argument is that nothing can be known except that it is some mind, and whatever is known without being in my mind must be in some other mind.

Russell presents a critique of Berkley's argument, starting with Berkley's notion of idea. Berkley defines an idea as something that is immediately known. Sensations are ideas; things we see and sounds we hear and so forth. Things we remember or imagine are also immediately known and so are also ideas. Berkley maintains that we can only know of objects in the world by perceiving them, that being is being perceived. Objects continue to exist when no one else perceives them because they remain in the mind of God.

Such a view of idea confuses the notion of being "in a mind". The thought of the object is in the mind but the thing itself is not. It seems like too simple a mistake to be made, but there are circumstances that led Berkley down this path.

Berkley does successfully demonstrate that sensation of physical objects is subjective. Without the observer, there would be no sensations. The sensations of an object therefore exist only in the mind of the observer. This is a step towards showing that to be known things must be mental. However, Berkley's idea conflates the thing apprehended with the apprehension itself. Because the perception is mental does not imply or require the thing being perceived to be mental. As Russell puts it:

...we readily assent to the view that ideas must be in the mind. Then, forgetting that this was only true when ideas were taken as acts of apprehension, we transfer the proposition that 'ideas are in the mind' to ideas in the other sense, i.e. to the things apprehended by our acts of apprehension. Thus, by an unconscious equivocation, we arrive at the conclusion that whatever we can apprehend must be in our minds.

Russell then turns his attention to a related notion in idealism, that of "we cannot know that anything exists which we do not know." Know is used in two different ways in the sentence and when this ambiguity is handled the sentence becomes clearly false. The "know" used in "we cannot know that anything exists..." is the know that means recognizing as true. This kind of knowledge is also called called judgement. The "know" in the second case is knowing about things, and is called acquaintance. The statement is then rendered as "we cannot make judgements about anything with which we are not acquainted." This is false, for, although we are not acquainted with Bertrand Russell or Bishop Berkley, we can certainly make judgements about them.

When something is not known by direct experience, or, in Russell's terminology, by acquaintance, it is known by description.

Knowledge by Acquaintance and Knowledge by Description

We know from the previous discussion of judgements and acquaintance, that there are two kinds of knowledge: knowledge of truths and knowledge of things. Knowledge of things is further partitioned into knowledge by acquaintance and knowledge by description. Knowledge by acquaintance is the simplest kind of knowledge. It is without reference to any truths and accessed by direct experience.

To given an example of knowledge by acquaintance Russell returns to the example of the table. The experience of the color of the table, is an experience of knowledge by acquaintance. There is nothing that can be added to the experience of the "brownness" of the table. It is immediately accessible and complete.

The table itself though, is not known to us by acquaintance. There are a set of sensations we associate with the table and we can, from these, create a description which only Russell's table will match. Thus the table is known to us by description.

Russell declares:

All our knowledge, both knowledge of things and knowledge of truths, rests upon acquaintance as its foundation.

The following are things we know by acquaintance:

direct sensation, as per earlier discussion

memory

introspection, as in "I am aware of my perception of the brownness of the table"

perhaps, although not certainly, the self

general ideas, such as motherhood

Having categorized what can be known by acquaintance, Russell turns to knowledge by description. Anything that is referred to a "a so-and-so" is an ambiguous description. Things that are referred to as "the so-and-so" are a definite description. Ambiguous descriptions are problematic and a definition of knowledge by description can be made without going into those problems. So Russell focuses on definite descriptions. A definite description is a set of properties that designate a particular object. Unless the object derives its existence from a logical analysis of the description, such as "the longest living man", some aspect of the description must be known to us by acquaintance. In fact, in the analysis of propositions made up of descriptions, each proposition which can be understood must consist entirely of constituents with which we are acquainted. If there were not the case we could not make any judgment about the proposition. For the words in the proposition must have some meaning and that meaning derives from acquaintance.

We are certain of knowledge we have by acquaintance, but such knowledge is private to us. Knowledge by description allows us to pass beyond the realm of private experience and gain knowledge of things we have not experienced.

On Induction

Given what we can know about things, Russell turns our attention to what we can infer. To do this he presents the judgement, "The sun will rise tomorrow."

What basis do we have to believe this is true? Our immediate answer is because it has always done so in the past, but this does not satisfy us with any certainty. Even if we appeal to science and the laws of motion our desire for certainty is not satisfied, for we should we believe that the laws of motion will continue to operate tomorrow as the have in the past?

The answer is that we do not know "for certain". As a kind of event A occurs together with a kind of event B and these two kinds of events never occur apart, each new occurrence increases the probability that these events will be related in the next occurrence. This probability approaches certainty, without limit.

Russell concludes the chapter by stating:

all knowledge which, on a basis of experience tells us something about what is not experienced, is based upon a belief which experience can neither confirm nor confute, yet which, at least in its more concrete applications, appears to be as firmly rooted in us as many of the facts of experience

The following chapter elaborates on other kinds of knowledge that, like induction, is assumed true but can not be proven true.

On Our Knowledge of General Principles

Russell next brings our attention to implication. The simple argument if A is true then B is true. A is true, so B must be true is generally accepted, but there is nothing in our experience to prove that it is true. Yet, without proof, we are as certain of it as we are of our sensations. In addition to implication, there are other self-evident principles that allow us to reason about propositions. These are called the laws of thought (though Russell finds the title misleading).

They are as follows:

(1) The law of identity: 'Whatever is, is.'

(2) The law of contradiction: 'Nothing can both be and not be.'

(3) The law of excluded middle: 'Everything must either be or not be.'

The title is misleading because it is not that we must think this way, but that when we do think this way, we think correctly.

The Empiricists and Rationalists schools of philosophy each have different views as to how to we come to know these general principles. The Empiricists believe that general principles arise out of experience. The rationalists believe that the general principles are inate ideas.

Russell declares that the rationalist are correct, in that experience can not prove these general principles are true, but that empiricists are correct in that our experience does suggest the principles. It would be ridiculous to suggest that the principles are inate in the sense babies are born knowing them. Experience clearly plays a role in giving us an understanding of these prinicples. Since the term inate has this notion of being born into this knowledge, philosopers use the term a priori.

How A Priori Knowledge is Possible

Immanuel Kant made significant contributions to the understanding of a priori knowledge. He showed that a priori knowledge can be synthetic, that is, new knowledge can be gained that is not implicit in the a priori proposition. Prior to Kant's work, it was general held that all a priori knowledge was analytic, that is any knowledge recognized from an a priori proposition was some how contained in the proposition and extracted by analysis.

David Hume, a slightly earlier contemporary of Kant's, had shown that cause could not be logically deduced from effect (contrary to what the rationalist school, in which Kant had studied, believed). Hume went on to propose that no a prior knowledge is possible about cause and effect. Kant countered this proposal by asserting that synthetic a priori knowledge is possible and indeed that all mathematics is synthetic a priori knowledge. Russell explains Kant's assertion by presenting Kant's stock example 7+5 = 12. No amount of analysis of 7 or of 5 will demonstrate the idea of 12. This proposition and all mathematical propostions are synthetic.

Having made and demonstrated this assertion, Russell explores Kant's answer to the question "How is mathematics possible?"

The problem arises through the fact that such knowledge is general, whereas all experience is particular. It seems strange that we should apparently be able to know some truths in advance about particular things of which we have as yet no experience; but it cannot easily be doubted that logic and arithmetic will apply to such things. We do not know who will be the inhabitants of London a hundred years hence; but we know that any two of them and any other two of them will make four of them. This apparent power of anticipating facts about things of which we have no experience is certainly surprising.

To explain this surprising result, Kant begins by distinguishing "the thing in itself", what Russell has called the physical object, and our sense data. Our experience of an object is a combination of our sense data and our own judgements about the sense data. This combination of sense data and judgements Kant refered to as "phenomenon". Since phenomena are a result of sense data and our own judgements and our judgements supply abstract concepts about the sense data, all our experience of the world is subject to reason, because nothing enters our experience which does not include the abstract judgements we supply.

Russell points out that by attributing logic and arithmetic to the observer, the problem of how mathematics is possible is not answered. This is because our own nature is changeable, where as logic and mathematics seems unchanging. If our nature is the source of mathematics, and our nature changes, then it might be possible that tomorrow 2+2 would be 5.

A priori knowledge involves concepts which can not be placed in the physical world. To give and example of a concept not in the physical world, consider the sentence "I am in my room". I am an entity in the physical world and so is my room, but "in" is not, at least not in the same way that "I" and "my room" are. The concept can not be attributed to the mind, either. For if an earwig is in my room, it is in my room whether I know it or not.

In the chapter The World of Universals, Russell then explores what these concepts, being neither mental nor physical, are.

The World of Universals

Plato gave an excellent account of universals in his "Theory of Ideas". When, for example, Plato seeks to define justice, he points out that we notice this or that just act, each of them has something in common and this commonality is justice. Russell clarifies that the idea here is not an idea in the sense that it is a thought, rather it is a pure form, the distillation of individual just acts. So though it is apprehended by minds, it is not a thought. To avoid confusion, Russell uses the term universal.

Universals are distinguished from particulars in that particulars are given by sensation. We experience a white thing or a just act. There is a commonality of white things which gives us the universal white. Proper nouns and pronouns are particulars while other nouns, verbs, adverbs and prepositions are universals. It is remarkable that no sentence can be constructed without the use of at least one universal.

Russell presents the following argument against the empiricists that deny the existence of universals. Suppose that there are no universals and that the idea of whiteness can only conceived of as a particular. Then when we examine how we know that any given thing is white, we discover that it must have a relationship to some other white thing. This relationship is a universal.

Universals have a unique sort of being in that while they are not sensations neither are they thoughts. Take, for example, the statement "Edinburgh is north of London". The statement is true whether there is any one who thinks it. The statement's truth does not depend on any ones apprehension of it. Further, if a universal were a thought we would

... rob it of its essential quality of universality. One man's act of thought is necessarily a different thing from another man's; one man's act of thought at one time is necessarily a different thing from the same man's act of thought at another time. Hence, if whiteness were the thought as opposed to its object, no two different men could think of it, and no one man could think of it twice. That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts.

Thus there are two realms of being, the realm of thoughts and sensations and the realm of universals. Our knowledge of universals relates these two realms.

On Our Knowledge of Universals

We have acquaintance with sensation that have a quality of color, texture and taste. When we experience something that is white and then some other sensation that also has that same color, it is easy to abstract out the universal "whiteness".

We also have acquaintance with relations between universals, and Russell demonstrates this through analysis of parts of a whole. Consider a page of paper. Some parts of the page are to the left of other parts, and some parts are above other parts. It is not difficult to see how we can abstract the concept of "to the left of" and "above" and "below" from acquaintance with our experiences. Similar arguments can be made for temporal relationships.

Having established what universals are and how we come to know them, Russell asserts that all a priori knowledge deals exclusively with the relationship of universals. He gives as an example of two and two are four, which he restates as "any collection formed of two twos is a collection of four". To see that this is a statement only about universals, we examine what words we must understand to understand the proposition. We can see that once we understand the words two, four and collection we will understand the proposition without any reference to any particular. The earlier question of how a priori knowledge can control or predict experience can now be seen to be a misapprehension. Although statements that involve a priori knowledge can be applied to particulars, it is understood without reference to them and so there is no control or prediction involved, only the relationship of universals. Russell goes on to demonstrate the interesting fact that knowledge of universals can give us knowledge about things we can, by definition, never know by experience.

Concluding this explanation of how a priori knowledge is possible, there is a survey of the kinds of knowledge discussed in the book up to this point. There is knowledge of things and knowledge of truths. There is knowledge by acquaintance and knowledge by description. In the category of knowledge by acquaintance, we have knowledge of sense-data, universals and perhaps knowledge of ourselves. In knowledge by description, we have some part whic is knowledge by acquaintance and some part which is knowledge of truths. Some knowledge of truths is known immediately. This kind of knowledge is called intuition.

On Intuitive Knowledge

We commonly believe that we should have reasons for our beliefs and although we may not be ready with the reasons we believe something, we generally feel we can supply reasons for our beliefs. If we explore what those reasons might be, we quickly come to some general principle, such as induction. As Russell presented in chapter six, such principles seem self evident and no reason can be given for believing them.

In addition to general principles that are self evident, we also have intuitive knowledge about our sense-data, in that no evidence can be offered for our belief, yet we are certain that it is true. There are "truths of perceptions", which are what we believe are our sense perceptions. "I see a red patch" is an example of a "truth of perception". There are also judgements of perception, such as "This red patch is round". Judgements of perception describe properties and relations of truths of perception.

There is a third kind of intuitive knowledge, judgements of memory. Russell defines memory as an object immediately before the mind which is recognized as past. Judgements of memory are similar in self evidence to other kinds of intuitive knowledge, but differ from those related to truths of perception and general principles in that they may be mistaken. From this observation we can see that self evidence has degrees of certainty. A general principle such as the law of the contradiction and a truth of perception have a near certain degree of self evidence. Memories of events that happened long ago, or which we did not attend to are much less certain.

Truth and Falsehood

The problem of what is true and what is false is difficult:

Since erroneous beliefs are often held just as strongly as true beliefs, it becomes a difficult question how they are to be distinguished from true beliefs. How are we to know, in a given case, that our belief is not erroneous? This is a question of the very greatest difficulty, to which no completely satisfactory answer is possible. There is, however, a preliminary question which is rather less difficult, and that is: What do we mean by truth and falsehood?

Russell presents three criteria for answering this question. A theory of truth must allow for beliefs to be false, as well as true. It must assign truth or falsehood to be a property of the belief and the truth value must depend on things outside the belief.

Russell then works through an example of false belief from Othello to establish the details for a theory of truth. A belief has object-terms, the things the belief is about and also object-relations, which describe how the object-terms are related to each other. A belief is true is there is a complex unity of the object-terms and object-relations that correspond to a fact. This is a precise way of saying that a belief is true if it corresponds to a fact and false if it does not.

Knowledge, Error and Probable Opinion

To know which of our beliefs are true and which are false requires that we first understand the definition of "to know". The simple definition that knowledge is true belief is insufficient. One may belief something that is true but believe it for reasons that are in error. Such a belief is a true belief but is not knowledge. To narrow the definition of knowledge to exclude this possibility Russell introduces the terms intuitive and derivative knowledge. "Derivative knowledge is what is validly deduced from premisses known intuitively" We know from chapter 11 that intuitive knowledge may range from certainty and near certainty in such cases as inference and relations between universals to doubtful as in the case of a memory of a long past event.

So, Russell concludes, firmly held beliefs that are true (beliefs that correspond to facts) are knowledge. Firmly held beliefs that do not correspond to facts are error. Beliefs which are neither knowledge or error are probable opinion. Coherence of beliefs give us more certainty about beliefs which held individually might seem doubtful.

The Limits of Philosophical Knowledge

Many metaphysical writers attempt to show from a priori principles some grand design to explain the nature of the world. In modern philosophy Hegel has been an influential example of this practice. Russell believes that such attempts are futile and that examining Hegel's system gives us some in sight as to why.

Russell's interpretation of Hegel, which he believes is widely held, is that everything short of the Whole is obviously fragmentary, and obviously incapable of existing without the complement supplied by the rest of the world. Both the world of things and the world of thought exhibit this fragmentary nature. In the world of things each thing seems to imply something larger and as we seek to understand the larger thing we eventually arrive at the universe as a whole. In the world of thought, the incompleteness appears as contradictions giving rise to the cycle of thesis anti-thesis and synthesis (the famous Hegelian Dialectic). Following this dialectic to its conclusion leads to the "Absolute Idea" which describes reality. This reality is one single harmonious system, not in space or time, not in any degree evil, wholly rational, and wholly spiritual. The flaw in Hegel's argument is equivocation with respect to the idea of the nature of things. Hegel uses the nature of things both to mean all the truths of something and the thing itself. To explain Russell gives an example of a tooth ache. The sufferer knows the nature of the tooth ache in a way the dentist does not. The sufferer does not know many of the truths about the tooth ache that the dentist does. It does not follow that the sufferer does not know the nature of the tooth ache because he or she does not know all the truths about the tooth ache.

Russell criticizes Hegel and others who start off with a view to prove and then construct a system to prove it. These philosophers try to show that some perceived aspect of reality is actually contradictory. But as knowledge advances, we find again and again that the contradictions vanish and with them the a priori knowledge of the world proposed by the philosopher.

Kant is another example of a philosopher that reasons that some aspect of reality is self contradictory. His target was space-time. Because apparent space and time are infinitely large and infinitely small, the seem to present contradictions. Infinity was very problematic for mathematicians and philosophers until the late 19th century. Kant, writing in the 18th century, saw these apparent contradictions and proposed that our experience of space-time was subjective. But infinity is not self contradictory and Kant's interpretation of space-time now appears to be incorrect.

<the relationship between logic and experience has changed>

For example, regarding space, it was formerly believed that the axioms of euclidean space are required by logic, but due to advances in mathematics, we now know that this is not true and the axioms of euclidean space only seem true due to our experience of the world. So,

Formerly it appeared that experience left only one kind of space to logic, and logic showed this one kind to be impossible. Now, logic presents many kinds of space as possible apart from experience, and experience only partially decides between them. Thus, while our knowledge of what is has become less than it was formerly supposed to be, our knowledge of what may be is enormously increased. Instead of being shut in within narrow walls, of which every nook and cranny could be explored, we find ourselves in an open world of free possibilities, where much remains unknown because there is so much to know.

<How knowledge by acquaintce and knowledge by description together with knowledge of universals make knowlege of the nature of the universe possible>

<science philosophy and criticism. contributions to knowledge through confirmation. limits of criticism. >

Thus, philosophy reduces the likelihood of error in our body of knowledge.

The Value of Philosophy

It is sometimes argued that philosophy is a pointless activity, arguing about things where no knowledge can be gained and contributing nothing to humanity. Russell presents his refutation of this argument and reasons why philosophy is a beneficial area of study for everyone.

Some endeavours, such as engineering, benefit even those not involved by virtue of the physical products they produce. Philosophy does not have this benefit, but does benefit those who study it, and may indirectly benefit others who are effected by the lives of those who do study it. A practical man may object that such a study does not provide shelter or put food on the table. Such a 'practical man' is one who recognizes the only materials needs of humanity, but ignores other needs. However, even if all of societies physical needs were met, there would still be unmet needs. "...even in the existing world the goods of the mind are at least as important as the goods of the body. " Philosophy is one of the fields that provides goods of the mind.

Philosophy aims at the kind of knowledge that gives unity and coherence to science. Progress in philosophy has been meger. This is in part due to the movements of fields out of the realm of philosophy once definite knowledge in the field becomes possible. When Newton wrote his Principia, it was a work of philosophy. Psychology has in the last 150 years moved out of the philosophy and into the sciences. But even excluding events like these, philosophy still has not provided many definite answers to the questions it raises. This is because philosophy inquires into things that by their nature do not allow for definite knowledge. It is not foreseeable how a question like Is consciousness a permanent part of the universe? could have a definite answer. Philosophy continues to examine such questions to keep alive speculative interests and keep before humanity the importance of such questions.

Without philosophy, our minds become dull and the world is uninteresting and common. We are unlikely to encounter new ideas, or if we do are unlikely to be receptive to them. Without philosophy the self is small and doomed to death.

Unless we can so enlarge our interests as to include the whole outer world, we remain like a garrison in a beleagured fortress, knowing that the enemy prevents escape and that ultimate surrender is inevitable. In such a life there is no peace, but a constant strife between the insistence of desire and the powerlessness of will. In one way or another, if our life is to be great and free, we must escape this prison and this strife.

By seeking philosophical knowledge we have the opportunity to expand ourselves, to become a free intellect.

The free intellect will see as God might see, without a here and now, without hopes and fears, without the trammels of customary beliefs and traditional prejudices, calmly, dispassionately, in the sole and exclusive desire of knowledge—knowledge as impersonal, as purely contemplative, as it is possible for man to attain. Hence also the free intellect will value more the abstract and universal knowledge into which the accidents of private history do not enter, than the knowledge brought by the senses, and dependent, as such knowledge must be, upon an exclusive and personal point of view and a body whose sense-organs distort as much as they reveal.

Having thus participated in such an intellectual undertaking it becomes possible to bring the experience back to daily life, behaving more justly, more lovingly and to live with a keen desire for truth. And so the study of philosophy makes the mind of its students great and capable of being identified not with the small self but with the universe as a whole.

Bibliographical Note

Russell recommends reading philosophers directly rather than reading about them in other philosophy texts. His recommendations are all available free on line: